"3.2 Of peas, pods and genes
When a physicist attempts to infer the properties of microscopic objects from macroscopic observations, ingenuity (in order to design meaningful experiments) must be combined with a good deal of logic (in order to deduce these microscopic properties from the macroscopic results). Obviously, some abstract reasoning is indispensable, merely because it is impossible to observe with the naked eye, or to take in one's hand, an electron or even a macromolecule for instance. The scientist of past centuries who, like Mendel, was trying to determine the genetic properties of plants, had exactly the same problem: he did not have access to any direct observation of the DNA molecules, so that he had to base his reasoning on adequate experiments and on the observation of their macroscopic outcome. In our parable, the scientist will observe the color of flowers (the "result" of the measurement, +1 for red, -1 for blue) as a function of the condition in which the peas are grown (these conditions are the "experimental settings" a and b, which determine the nature of the measurement). The basic purpose is to infer the intrinsic properties of the peas (the EPR "element of reality") from these observations.

3.2.1 Simple experiments; no conclusion yet.
It is clear that many external parameters such as temperature, humidity, amount of light, etc. may influence the growth of vegetables and, therefore, the color of a flower; it seems very difficult in a practical experiment to be sure that all the relevant parameters have been identified and controlled with a sufficient accuracy. Consequently, if one observes that the flowers which grow in a series of experiments are sometimes blue, sometimes red, it is impossible to identify the reason behind these fluctuation; it may reflect some trivial irreproducibility of the conditions of the experiment, or something more fundamental. In more abstract terms, a completely random character of the result of the experiments may originate either from the fluctuations of uncontrolled external perturbations, or from some intrinsic property that the measured system (the pea) initially possesses, or even from the fact that the growth of a flower (or, more generally, life?) is fundamentally an indeterministic process - needless to say, all three reasons can be combined in any complicated way. Transposing the issue to quantum physics leads to the following formulation of the question: are the results of the experiments random because of the fluctuation of some uncontrolled influence taking place in the macroscopic apparatus, of some microscopic property of the measured particles, or of some more fundamental process?

The scientist may repeat the "experiment" a thousand times and even more: if the results are always totally random, there is no way to decide which interpretation should be selected; it is just a matter of personal taste. Of course, philosophical arguments might be built to favor or reject one of them, but from a pure scientific point of view, at this stage, there is no compelling argument for a choice or another. Such was the situation of quantum physics before the EPR argument.

3.2.2 Correlations; causes unveiled.
The stroke of genius of EPR was to realize that correlations could allow a big step further in the discussion. They exploit the fact that, when the choice of the settings are the same, the observed results turn out to be always identical; in our botanical analogy, we will assume that our botanist observes correlations between colors of flowers. Peas come together in pods, so that it is possible to grow peas taken from the same pod and observe their flowers in remote places. It is then natural to expect that, when no special care is
taken to give equal values to the experimental parameters (temperature, etc.), nothing special is observed in this new experiment. But assume that, every time the parameters are chosen to the same values, the colors are systematically the same; what can we then conclude? Since the peas grow in remote places, there is no way that they can be influenced by the any single uncontrolled fluctuating phenomenon, or that they can somehow influence each other in the determination of the colors. If we believe that causes always act locally, we are led to the following conclusion: the only possible explanation of the common color is the existence of some common property of both peas, which determines the color; the property in question may be very difficult to detect directly, since it is presumably encoded inside some tiny part of a biological molecule, but it is sufficient to determine the results of the experiments.

Since this is the essence of the argument, let us make every step of
the EPR reasoning completely explicit, when transposed to botany. The
key idea is that the nature and the number of "elements of reality"
associated with each pea can not vary under the influence of some
remote experiment, performed on the other pea. For clarity, let us first assume that the two experiments are performed at different times: one week, the experimenter grows a pea, then only next week another pea from the same pod; we assume that perfect correlations of the colors are always observed, without any special influence of the delay between the experiments. Just after completion of the first experiment (observation of the first color), but still before the second experiment, the result of that future experiment has a perfectly determined value; therefore, there must already exist one element of reality attached to the second pea that corresponds to
this fact - clearly, it can not be attached to any other object than the pea, for instance one of the measurement apparatuses, since the observation of perfect correlations only arises when making measurements with peas taken from the same pod. Symmetrically, the first pod also had an element of reality attached to it which ensured that its measurement would always provide a result that coincides with that of the future measurement. The simplest idea that comes to mind is to assume that the elements of reality associated with both peas are coded in some genetic information, and that the values of the codes are exactly the same for all peas coming from the same pod; but other possibilities exist and the precise nature and mechanism involved in the elements of reality does not really matter here. The important point is that, since these elements of reality can not appear by any action at a distance, they necessarily also existed before any measurement was performed - presumably even before the two peas were separated.

Finally, let us consider any pair of peas, when they are already spatially separated, but before the experimentalist decides what type of measurements they will undergo (values of the parameters, delay or
not, etc.). We know that, if the decision turns out to favor time separated measurements with exactly the same parameter, perfect correlations will always be observed. Since elements of reality can not appear, or change their values, depending of experiments that are performed in a remote place, the two peas necessarily carry some elements of reality with them which completely determine the color of the flowers; any theory which ignores these elements of reality is incomplete. This completes the proof.

It seems difficult not to agree that the method which led to these conclusions is indeed the scientific method; no tribunal or detective would believe that, in any circumstance, perfect correlations could be observed in remote places without being the consequence of some common characteristics shared by both objects. Such perfect correlations can then only reveal the initial common value of some variable attached to them, which is in turn a consequence of some fluctuating common cause in the past (a random choice of pods in a bag for instance). To express things in technical terms, let us for instance assume that we use the most elaborate technology available to build elaborate automata, containing powerful modern computers if necessary, for the purpose of reproducing the results of the remote experiments: whatever we do, we must ensure that, somehow, the memory of each computer contains the encoded information concerning all the
results that it might have to provide in the future (for any type of
measurement that might be made).

To summerize this section, we have shown that each result of a measurement may be a function of two kinds of variables:

(i) intrinsic properties of the peas, which they carry along with them.
(ii) the local setting of the experiment (temperature, humidity, etc.);
clearly, a given pair that turned out to provide two blue flowers could have provided red flowers in other experimental conditions. We may also add that:
(iii) the results are well-defined functions, in other words that no
fundamentally indeterministic process takes place in the experiments.
(iv) when taken from its pod, a pea cannot "know in advance" to which sort of experiment it will be submitted, since the decision may not yet have been made by the experimenters; when separated, the two peas therefore have to take with them all the information necessary to determine the color of flowers for any kind of experimental conditions. What we have shown actually is that each pea carries with it as many elements of reality as necessary to provide "the correct answer" to all possible questions it might be submitted to."

Embarrassing. We all understand the "common sense" of the local realistic position. That and a quarter will get you 25 cents.

1) What are you saying, other than quoting other people? Are we to deduce from the quote that it is an exact representation of your position? Or are you being coy, and hoping we will misread your position? If you have something to say, why won't you say it? (That is normally incumbent on those who start threads.)

2) How do peas prove EPR? You are going to have to do better than that. We understand that some people hypothesize the existence of little teeny tiny attributes that we cannot see. Most of us call those "hidden variables" and don't need to call them pea DNA by childish analogy. We also understand that no-one knew about DNA a few hundred years ago. Also a poor analogy.

EPR envisioned that the so-called hidden variables would eventually be uncovered. That hasn't happened in 80 years of looking. Instead, it has become obvious to scientists that there is no combination of hidden variables that can mimic the results of certain experiments (per Bell). Please tell us - SPECIFICALLY and not hand waving - how you conclude otherwise. If there is an "element of reality" we are missing, please, do show us. I, for one, am all ears.

EPR never said ANYTHING about hidden variables - if you can find one instance of EPR talking about hidden variables, I will give you my car.

All the best
John B.

What kind of car do you have?

"While we have thus shown that the wave function does not provide a complete specification of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible."-EPR

If the more complete description is dependent on finding something which is now hidden, I would call that "hidden variables". The definition of "hidden variables" is usually taken to be those variables which supply the missing description.

It certainly isn't pea DNA, and I notice that you completely sidestep all of my questions as per your usual. Do you have any position? Or is your objective to stir controversy?

EPR never said ANYTHING about hidden variables - if you can find one instance of EPR talking about hidden variables, I will give you my car.

All the best
John B.

They used the phrase "element of reality", and made it clear that they believe there is an element of reality corresponding to the value of both of two physical properties with noncommuting operators, like position and momentum--this exactly what is meant by "hidden variables". From the EPR paper:

Previously we proved that either (1) the quantum-mechanical description of reality given by the wave function is not complete or (2) when the operators corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality. Starting then with the assumption that the wave function does give a complete description of the physical reality, we arrived at the conclusion that two physical quantities, with noncommuting operators, can have simultaneous reality. Thus the negation of (1) leads to the negation of the only other alternative (2). We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete.

One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive. Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted. On this point of view, since either one or the other, but not both simultaneously, of the quantities P and Q can be predicted, they are not simultaneously real. This makes the reality of P and Q depend upon the process of measurement carried out on the first system, which does not disturb the system in any way. No reasonable definition of reality could be expected to permit this.

While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible.

So, they reject the view that position Q and momentum P are not both elements of reality which exist prior to the measurement of the entangled particle--this means they are arguing for hidden variables.

No "hidden variables" were needed. All Bohr had to do in order to complete QM was admit the calculated (unobserved) variable - Einstein claimed that if he could predict it with probabiliy 1, then the calculated (unobserved) variable was an "element of reality", that is, it was as valid as the observed variable. Bohr would not agree to this since it would invalidate Heisenberg uncertainty. So, no hidden variables were ever needed. This is just one more example of QM people putting words in Einsteins mouth.

No "hidden variables" were needed. All Bohr had to do in order to complete QM was admit the calculated (unobserved) variable - Einstein claimed that if he could predict it with probabiliy 1, then the calculated (unobserved) variable was an "element of reality", that is, it was as valid as the observed variable. Bohr would not agree to this since it would invalidate Heisenberg uncertainty. So, no hidden variables were ever needed. This is just one more example of QM people putting words in Einsteins mouth.

But that's what the phrase "hidden variables" means--don't get hung up on the word "hidden", it just means "a variable not directly measured, although some may believe its value can be inferred".

Do you agree that if Bell's theorem is violated in an experiment involving spin measurements, then it is impossible to explain the results of the experiment using the idea that each spin-value had a preexisting value without giving up locality?

No, if Einstein's Principle of Local Action is not valid, then neither is experimental science.

So does that mean you think it is impossible for Bell's theorem to be violated? Or do you disagree that a violation of Bell's theorem discredits any theory that postulates that all these variables have preexisting values and also respects the principle of local action?

Also, what do you think of Bohmian mechanics? This is a deterministic interpretation of QM which says particles have a definite position at all times (even when we measure their momentum), and which includes faster-than-light effects, but nevertheless can be proven to make all the same predictions as ordinary QM.

No, if Einstein's Principle of Local Action is not valid, then neither is experimental science.

I would say that this is the most moronic thing I have ever seen written, but that wouldn't be a nice thing to say.

Reality is what it is. It certainly does not matter to reality whether your purely semantic argument is correct. Meanwhile, the results of experiments are exactly as Bohr envisioned. So who has the last laugh? How do experiments of entangled particles correlate in violation of Bell?

There are hidden variables in classical statistical mechanics of coin-tossing. It's perfectly deterministic. But due to our ignorance of the intricate details of its complete dynamics, we lump them all into statistical probabilities. Thus, all those intricate dynamics are hidden from the statistical description of coin-tossing.

Einstein is claiming the same thing. He said that there has to be some underlying mechanism of QM that is not included in its formulation. So these are hidden from the theory. In fact, this idea was later on used by Bohm as the hidden variables.[1]

Irregardless of what you think, there has been no controversies till now that the EPR paper is in fact claiming that QM is incomplete, and that this is due to variables not contained within the formalism. They may not explicitly use the pharse "hidden variables", but the implied presence of them has never been disputed within this paper.

Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted. On this point of view, since either one or the other, but not both simultaneously, of the quantities P and Q can be predicted, they are not simultaneously real. This makes the reality of P and Q depend upon the process of measurement carried out on the first system, which does not disturb the system in any way. No reasonable definition of reality could be expected to permit this.

It is pretty clear from the experimental record: A measurement at one system determines the "reality" of the observable at the other. For spin entanglement, there is complete reality only when the polarizers are at 0 or 90 degrees. That is our "element of reality."

Aside from what ZapperZ said, "hidden variables" is just a technical term, as long as all physicists understand what this term means in the context of QM, it doesn't matter if the words completely match their ordinary-english meaning. It's like how the "flavor" of a quark doesn't have anything to do with the ordinary meaning of the word "flavor".

And you still haven't answered my question--do you think it is impossible that Bell's theorem can ever be violated, or do you just deny that a violation of Bell's theorem discredits "local hidden variables", meaning the idea that noncommuting variables like position and momentum all have exact values even when we don't measure them, and that no influences can go faster than light?

The fact is that the quantum community has revised the Einstein side of the EPR argument to fit their desires for the past 75 years. I think the TRUTH is a better approach. When someone says that Einstein said something, that something should be what Einstein said.

Bell's 4 dimensional Hilbert space has almost nothing to do with the real world. As far as the Bell Test experiments, until a more mature model of the photon is developed, the Bell Test experiments will prove nothing. Are you familiar with the single photon interference experiments (a photon undergoing interference with itself).

The fact is that the quantum community has revised the Einstein side of the EPR argument to fit their desires for the past 75 years. I think the TRUTH is a better approach. When someone says that Einstein said something, that something should be what Einstein said.

They haven't revised anything. Einstein believed that particles have definite values of position and momentum (and other noncommuting variables) at all times, even when we don't measure them, and that's what quantum physicists mean by the technical term "hidden variables". Again, it's unimportant whether the words match their ordinary english meaning, they could have called it "electric ostriches", and as long as all physicists knew what was meant by that term in the context of QM, it wouldn't matter that exact simultaneous values for noncommuting variables have nothing to do with large flightless birds.

JohnBarchak said:

Bell's 4 dimensional Hilbert space has almost nothing to do with the real world. As far as the Bell Test experiments, until a more mature model of the photon is developed, the Bell Test experiments will prove nothing. Are you familiar with the single photon interference experiments (a photon undergoing interference with itself).

Bell's inequality has nothing to do with any "4 dimensional Hilbert space", it is just based on basic logic and probability. Here's a quickie explanation of the meaning of Bell's Theorem I wrote up on another forum. First, check out this analogy from the book Time's Arrow and Archimedes' Point:

By modern standards the criminal code of Ypiaria [pronounced, of course, "E-P-aria"] allowed its police force excessive powers of arrest and interrogation. Random detention and questioning were accepted weapons in the fight against serious crime. This is not to say the police had an entirely free hand, however. On the contrary, there were strict constraints on the questions the police could address to anyone detained in this way. One question only could be asked, to be chosen at random from a list of three: (1) Are you a murderer? (2) Are you a thief? (3) Have you committed adultery? Detainees who answered "yes" to the chosen question were punished accordingly, while those who answered "no" were immediately released. (Lying seems to have been frowned on, but no doubt was not unknown.)

To ensure that these guidelines were strictly adhered to, records were required to be kept of every such interrogation. Some of these records have survived, and therein lies our present concern. The records came to be analyzed by the psychologist Alexander Graham Doppelganger, known for his work on long distance communication. Doppelganger realized that among the many millions of cases in the surviving records there were likely to be some in which the Ypiarian police had interrogated both members of a pir of twins. He was interested in whether in such cases any correlation could be observed between the answers given by each twin.

As we now know, Doppelganger's interest was richly rewarded. He uncovered the two striking and seemingly incompatible correlations now known collectively as Doppelganger's Twin Paradox. He found that

(8.1) When each member of a pair of twins was asked the same question, both always gave the same answer;

and that

(8.2) When each member of a pair of twins was asked a different question, they gave the same answer on close to 25 percent of such occasions.

It may not be immediately apparent that these results are in any way incompatible. But Doppelganger reasoned as follows: 8.1 means that whatever it is that disposes Ypiarians to answer Y or N to each of the three possible questions 1, 2, and 3, it is a disposition that twins always have in common. For example, if YYN signifies the property of being disposed to answer Y to questions 1 and 2 and N to question 3, then correlation 8.1 implies that if one twin is YYN then so is his or her sibling. Similarly for the seven other possible such states: in all, for the eight possible permutations of two possible answers to three possible questions. (The possibilities are the two homogeneous states YYY and NNN, and the six inhomogeneous states YYN, YNY, NYY, YNN, NYN, and NNY.)

Turning now to 8.2, Doppelganger saw that there were six ways to pose a different question to each pair of twins: the possibilities we may represent by 1:2, 2:1, 1:3, 3:1, 2:3, and 3:2. (1:3 signifies that the first twin is asked question 1 and the second twin question 3, for example.) How many of these possibilities would produce the same answer from both twins? Clearly it depends on the twins' shared dispositions. If both twins are YYN, for example, then 1:2 and 2:1 will produce the same response (in this case, Y) and the other four possibilities will produce different responses. So if YYN twins were questioned at random, we should expect the same response from each in about 33 percent of all cases. And for homogeneous states, of course, all six posible question pairs produce the same result: YYY twins will always answer Y and NNN twins will always answer N.

[Note--I think Price actually gets the probability wrong here. If both twins are YYN, for example, then if they are questioned at random, the probability both will give the same answer would be P(first twin answers Y)*P(second twin answers Y) + P(first twin answers N)*P(second twin answers N) = (2/3)*(2/3) + (1/3)*(1/3) = 5/9, not 1/3 as Price claims. But this doesn't change the overall argument. edit: as Bartholomew pointed out below, I was misunderstanding Price here, he's actually calculating the probability the twins will give the same answer only in the subset of cases where they were asked different questions, not in all cases as I mistakenly assumed]

Hence, Doppelganger realized, we should expect a certain minimum correlation in these different question cases. We cannot tell how many pairs of Ypiarian twins were in each of the eight possible states, but we can say that whatever their distribution, confessions should correlate with confessions and denials with denials in at least 33 percent of the different question interrogations. For the figure should be 33 percent if all the twins are in inhomogeneous states, and higher if some are in homogeneous states. And yet, as 8.2 describes, the records show a much lower figure.

Doppelganger initially suspected that this difference might be a mere statistical fluctuation. As newly examined cases continued to confirm the same pattern, however, he realized that the chances of such a variation were infinitesimal. His next thought was therefore that the Ypiarian twins must generally have known what question the other was being asked, and determined their answer partly on this basis. He saw that it would be easy to explain 8.2 if the nature of one's twin?'s question could influence one's own answer. Indeed, it would be easy to make a total anticorrelation in the different question cases be compatible with 8.1--with total correlation in the same question cases.

Doppelganger investigated this possibility with some care. He found, however, that twins were always interrogated separately and in isolation. As required, their chosen questions were selected at random, and only after they had been separated from one another. There therefore seemed no way in which twins could conspire to produce the results described in 8.1 and 8.2. Moreover, there seemed a compelling physical reason to discount the view that the question asked of one twin might influence the answers given by another. This was that the separation of such interrogations was usually spacelike in the sense of special relativity; in other words, neither interrogation occurred in either the past or the future light cone of the other. (It is not that the Ypiarian police force was given to space travel, but that light traveled more slowly in those days. The speed of a modern carrier pigeon is the best current estimate.) Hence according to the principle of the relativity of simultaneity, there was no determinate sense in which one interrogation took place before the other.

The situation in one version of the EPR experiment is almost exactly like the situation with these imaginary Ypiarian twins, except that instead of interrogators having a choice of 3 crimes to ask the twins about, experimenters can measure the "spin" of two separated electrons along one of three axes, which we can label a, b, and c (this is not the only type of EPR experiment--the one that is usually tested experimentally is one involving photons called the Aspect experiment--but I'm discussing this one because it's so similar to the 'Ypiarian twin' analogy above). Whichever axis the experimenter chooses, she will find that the electron is either "spin-up" (+) or "spin-down" (-) along that axis, and if the other experimenter chooses to measure his own electron along the same axis, then when they compare results they will always find the electrons had opposite spins on that axis (you can only choose one of the three axes to measure though, because there is an uncertainty relation between spin on each axis similar to the position-momentum uncertainty relation). One might try to explain this by saying the electrons each started out with a well-defined spin along all three axes, with each having the opposite spin as the other along all three; for example, if you imagine one electron's spins along axes a, b and c were + - +, then the second electron's spins must have been - + -. But if you make this assumption that each had a well-defined spin along each axis, then some simple math shows that something called "Bell's Inequality" would be expected to hold. As this wikipedia entry on Bell's Theorem explains:

Each row describes one type of electron pair, with their respective hidden variable values and their probabilites N. Suppose Alice measures the spin in the a direction and Bob measures it in the b direction. Denote the probability that Alice obtains +1/2 and Bob obtains +1/2 by

P(a+,b+) = N3 + N4

Similarly, if Alice measures spin in a direction and Bob measures in c direction, the probability that both obtain +1/2 is

P(a+,c+) = N2 + N4

Finally, if Alice measures spin in c direction and Bob measures in b direction, the probability that both obtain the value +1/2 is

P(c+,b+) = N3 + N7

The probabilities N are always non-negative, and therefore:

N3 + N4 <= N3 + N4 + N2 + N7

This gives

P(a+,b+) <= P(a+,c+) + P(c+,b+)

which is known as a Bell inequality. It must be satisfied by any hidden variable theory obeying our very broad locality assumptions.

But in reality, the Bell inequalities are consistently violated in the EPR experiment--you get results like P(a+, b+) > P(a+,c+) + P(c+,b+). Again, this shows that you can't just assume each pair of electrons had well-defined opposite spins on each axis before you measured them, despite the fact that whenever the two experimenters choose to measure along the same axis, they always find the two electrons have opposite spins on that axis. There are some ways to save the idea that the particle has a well-defined state before measurement, but only at the cost of bringing in ideas like faster-than-light communication between the electrons or the choice of measurements retroactively influencing the states of the two particles when they were created.

No, he was right. He had the proviso that the questions asked each twin were not the same. This gives the correct probability: 2 cases / 6 cases or 1/3.

Ah, I didn't catch that. Still, it seems like the connection with EPR-type experiments would be better if you assume each interrogator picks his question at random right before he asks it to the twin he's interrogating, so that when each twin answers there's no way he could know anything about what question his brother was asked (assuming information can't travel faster than light).

edit: Or perhaps he meant that the experimenters do choose their questions randomly right before they ask them, but that we restrict our attention to the subset of cases where they randomly happened to ask different questions, and throw out the other 1/3 of cases where they happened to ask the same question. Out of this subset, a "hidden-variables" theory where you assume the twins had already decided on answers to all three questions would indeed predict that they'd give the same answer in at least 1/3 of the interrogations.

EPR envisioned that the so-called hidden variables would eventually be uncovered. That hasn't happened in 80 years of looking. Instead, it has become obvious to scientists that there is no combination of hidden variables that can mimic the results of certain experiments (per Bell).

You mean, no hidden variable theory can predict the correct answers for the Bell/EPR correlation experiments? That's just plain false. Bohmian mechanics does so.

Or maybe you meant that no hidden variable theory which respects Bell's Locality condition can predict the correct answers for such experiments. That's true; it's Bell's theorem.

But this is no argument against hidden variable theories, since orthodox QM itself violates Bell Locality. Remember, Bell Locality essentially amounts to the idea that joint probabilities for space-like separated events should factorize when you conditionalize on a complete specification (call it "L") of the world in the past light cones of the two events. Mathematically,

P(A,B|a,b,L) = P(A|a,L)*P(B|b,L)

where A and B refer to measurement outcomes, a and b refer to any other relevant parameters local to the two measurements respectively, and L is the complete specification across the past light cones.

Bohr (and all subsequent opponents of hidden variables) invites us to identify L with the quantum mechanical wave function psi. But according to QM,

And it is therefore a tragic (but admittedly widespread) mistake to argue against hidden variable theories on the grounds that they have to be non-local. Show me a theory that agrees with experiment and *is* local, then that objection might hold some water. But if one's only alternative to the (allegedly) preposterous-because-nonlocal hidden variable theories is orthodox QM itself, well, one would be shooting oneself in one's own foot...

And it is therefore a tragic (but admittedly widespread) mistake to argue against hidden variable theories on the grounds that they have to be non-local. Show me a theory that agrees with experiment and *is* local, then that objection might hold some water.

I came across this paper which seems to argue (although I may be misunderstanding) that you can get such a local description of the universe's state if you use the Heisenberg picture, where it's the operators that change over time rather than the wavefunction:

In the Everett interpretation the nonlocal notion of reduction of the wavefunction is eliminated, suggesting that questions of the locality of quantum mechanics might indeed be more easily addressed. On the other hand, while wavefunctions do not suffer reduction in the Everett interpretation, nonlocality nevertheless remains present in many accounts of this formulation. In DeWitt’s (1970) often-quoted description, for example, “every quantum transition taking place on every star, in every galaxy, in every remote corner of the universe is splitting our local world on earth into myriads of copies of itself.” Contrary to this viewpoint, others argue (Page, 1982; Tipler, 1986, 2000; Albert and Loewer, 1988; Albert, 1992; Vaidman, 1994, 1998, 1999; Price, 1995; Lockwood, 1996; Deutsch, 1996; Deutsch and Hayden, 2000) that the Everett interpretation can in fact resolve the apparent contradiction between locality and quantum mechanics. In particular, Deutsch and Hayden (2000) apply the Everett interpretation to quantum mechanics in the Heisenberg picture, and show that in EPRB experiments,1 information regarding the correlations between systems is encoded in the Heisenberg-picture operators corresponding to the observables of the systems, and is carried from system to system and from place to place in a local manner. The picture which emerges is not one of measurement-type interactions “splitting the universe” but, rather, producing copies of the observers and observed physical systems which have interacted during the (local) measurement process (Tipler, 1986).

Likewise, in this paper by the same author, I think he's arguing that the Everett interpretation of quantum field theory can also be understood in terms of information encoded in purely local operators:

In the Everett interpretation, correlations between the two experimenters’ results are not at issue; rather, a different question of causation arises. According to Everett, both possible outcomes, spin-up and spin-down, occur at each analyzer magnet and, at the conclusion of the experiment, there are two copies of each experimenter.2 When they compare their respective results using some causal means of communication, Alice-who-saw-spin-up only talks to Bob-who-saw-spin-down, and Alice-who-saw-spin-down always converses with Bob-who-saw-spin-up. What is the mechanism which brings about this perfect anticorrelation in the possibilities for exchange of information between the Alices and the Bobs?

Deutsch and Hayden(21) have identified this mechanism. In the Heisenberg picture of quantum mechanics, the properties of physical systems are represented by time-dependent operators. When two systems interact, the operators corresponding to the properties of each of the systems may acquire nontrivial tensor-product factors acting in the state space of the other system. These factors are in effect labels, appending to each system a record of the fact that it has interacted with a certain other system in a certain way.(22) So, for example, when the two particles in the EPRB experiment are initially prepared in the singlet state, the interaction involved in the preparation process causes the spin operators of each particle to contain nontrivial factors acting in the space in which the spin operators of the other particle act. When Alice measures the spin of one of the particles, the operator representing her state of awareness ends up with factors which act in the state space of the particle which she has measured, as well as in the state space of the other particle. The operator corresponding to Bob’s state of awareness is similarly modified. When the Alices and Bobs meet to compare notes, it is these factors which lead to the correct pairing-up of the four of them.

The amount of information which even a simple electron carries with it regarding the other particles with which it has interacted is thus enormous. In Ref. 22 I termed this the problem of “label proliferation,” and suggested that the physical question of how all this information is stored3 might receive an answer in the framework of quantum field theory.

More generally, quantum field theory is a description of nature encompassing a wider range of physical phenomena than the quantum mechanics of particles; it is therefore of interest to investigate the degree to which the conceptual picture of the labeling mechanism for bringing about correlations at a distance in a causal manner accords with the field-theoretic formalism.

Indeed, there is a simple line of argument which leads to the conclusion that Everett interpretation Heisenberg-picture quantum field theory must be local. The dynamical variables of the theory are field operators defined at each point in space, whose dynamical evolution is described by local (Lorentz-invariant, in the relativistic case) differential equations. And the Everett interpretation removes nonlocal reduction of the wavefunction from the formalism. So how can nonlocality enter the scene?

This argument as it stands is incorrect, but it can be modified so that its conclusion, the locality of Everett-interpretation Heisenberg-picture quantum field theory, holds. What is wrong is the following: While it is certainly true that operators in Heisenberg-picture quantum field theory evolve according to local differential equations, it is not in general true that all of the information needed to determine the outcomes and probabilities of measurements is contained in these operators. Initial-condition information, needed to determine probabilities, resides in the time-independent Heisenberg-picture state vector. Since not all information is carried in the operators, is incorrect to argue that the local evolution of the operators implies locality of the theory.

However, as discussed in Sec. 4 below, it turns out to be possible to transform from the usual representation of the Heisenberg-picture field theory to other representations in which the operators also carry the initial-condition information. So, in these representations, the simple argument above for the locality of Heisenberg-picture quantum field theory is valid. Bear in mind that in these representations the use of the Everett interpretation still is crucial for the theory to be local. As mentioned above, the Everett interpretation removes a source of explicit nonlocality in the theory (wavefunction collapse); it “defangs” the Bell argument that, notwithstanding the explicitly local transfer of information in the operators, something else of a nonlocal nature must be going on; and it provides labeling as an alternative to the “instruction set” mechanism which in single-outcome interpretations appears as the only explanation for correlations-at-a-distance and which is what ultimately leads to Bell’s theorem. This last issue of instruction sets and labels is no different in field theory than in first-quantized theory, and is discussed in Ref 22. In field theory as in first-quantized theory, interaction-induced transformations of Heisenberg-picture operators (field operators, of course, in the field theory case—see e.g., eq. (154) below) serve to encode the label information.

I also came up with this analogy to think about how an Everett-type interpretation might in principle be able to explain violations of Bell's theorem in a local way:

say Bob and Alice are each recieving one of an entangled pair of photons, and their decisions about which spin axis to measure are totally deterministic, so the only "splitting" necessary is in the different possible results of their measurements. Label the three spin axes a, b, and c. If they always find opposite spins when they both measure their photons along the same axis, a local hidden-variables theory would say that if they choose different axes, the probability they get opposite spins must be at least 1/3 (assuming there's no correlation between their choice of which axes to measure and the states of the photons before they make the measurement). I forgot what the actual probability of opposite spins along different axes ends up being in this type of experiment, but all that's important is that it's less than 1/3, so for the sake of the argument let's say it's 1/4.

So suppose Bob's decision will be to measure along axis a, and Alice's decision will be to measure along axis c. When they do this, suppose each splits into 8 parallel versions, 4 measuring spin + and 4 measuring spin -. Label the 8 Bobs like this:

Note that the decision of how they split is based only on the assumption that each has a 50% chance of getting + and a 50% chance of getting - on whatever axis they choose, no knowledge about what the other one was doing was needed. And again, only when a signal travelling at the speed of light or slower passes from one to the other does the universe need to decide which Alice shares the same world with which Bob...when that happens, they can be matched up like this:

This insures that each one has a 3/4 chance of finding out the other got the same spin, and a 1/4 chance that the other got the opposite spin. If Bob and Alice were two A.I.'s running on classical computers in realtime, you could simulate Bob on one computer and Alice on another, make copies of each according to purely local rules whenever each measured a quantum particle, and then use this type of matching rule to decide which of the signals from the various copies of Alice will be passed on to which copy of Bob, and you wouldn't have to make that decision until the information from the computer simulating Alice was actually transmitted to the computer simulating Bob. So using purely local rules you could insure that, after many trials like this, a randomly-selected copy of A.I. Bob or A.I. Alice would record the same type of statistics that's seen in the Aspect experiment, including the violation of Bell's inequality.

Note that you wouldn't have to simulate any hidden variables in this case--you only have to decide what the spin was along the axes each one measured, you never have to decide what the spin along the other 2 unmeasured axes of each photon was.

Now, I realize that the various Everett interpretations are not so straightforward--in my computer simulation above, probability has a clear frequentist meaning, while the problem of getting a notion of "probability" out of any version of the Everett interpretation is notoriously difficult, and perhaps it can't work at all without tacking on extra assumptions. Still, I got the impression that this was the general type of explanation that Mark Rubin was aiming for in his papers, where each observation creates a local splitting of the observer, but the observations of spatially separated observers are only mapped to each other once a signal has had the chance to pass between them.